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A Real Options Approach Using the Binomial Tree Method

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A Real Options Approach Using the Binomial Tree Method Valuation of Carbon Forestry and the New Zealand Emissions Trading Scheme: A Real Options Approach Using the Binomial Tree Method James Tee1, Riccardo Scarpa1, Dan Marsh1 and Graeme Guthrie2 1 Department of Economics, University of Waikato, New Zealand. 2 School of Economics and Finance, Victoria University of Wellington, New Zealand. Please kindly address all correspondences to [email protected] Selected Paper prepared for presentation at the International Association of Agricultural Economists (IAAE) Triennial Conference, Foz do Iguaçu, Brazil, 18-24 August, 2012. Reference number: 16930 Copyright 2012 by James Tee, Riccardo Scarpa, Dan Marsh and Graeme Guthrie. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. Abstract Under the New Zealand Emissions Trading Scheme, new forests planted on/after 1st January 1990 can earn carbon credits. These credits have to be repaid upon forest harvest. This paper analyses the effects of this carbon scheme on the valuation of bareland, on which radiata pine is to be planted. NPV/LEV and Real Options methods are employed, assuming stochastic timber and carbon prices. Valuation increases significantly and rotation age is likely to be lengthened. We include a scenario analysis of potential implications of rotation age lengthening on carbon stock management in New Zealand. 1 Introduction In order to meet New Zealand’s Kyoto Protocol commitments, its government passed cap-and-trade legislation, called the New Zealand Emissions Trading Scheme (NZETS), to create a carbon price and put in place incentives for businesses and consumers to change their behaviour. The NZETS is the world’s first economy-wide cap-and-trade system that covers all sectors and all gases. It is internationally linked as it reflects international climate change rules (New Zealand Government, 2010). The NZETS legislation includes a transition period between 1st July 2010 and 31st December 2012, during which emitters have been able to buy emission units (carbon credits) from the New Zealand government for a fixed price of $25 per unit (where 1 unit = 1 ton of carbon dioxide equivalent). In addition, emitters will only have to surrender one emission unit for every two tons of emissions they produce during this period. For the forestry sector, new forests established on and after 1st January 1990 are eligible to earn carbon credits1. Known domestically as post-1989 forests, these forests can earn carbon credits for increases in carbon stocks from 1st January 20082. If the carbon stock in a post-1989 forest decreases (for example, due to harvesting), emission units must be surrendered (i.e. harvest liabilities). These post-1989 forestry NZETS rules have been designed to directly reflect the rules of afforestation and reforestation under Article 3.3 of the Kyoto Protocol (UNFCCC, 1998). For forest owners, the new revenue stream from carbon credits and harvest liabilities alters the traditional timber-only cash flow business model, and affects the harvesting decision. After receiving the credits, they can be accumulated or immediately sold in domestic and international carbon markets, thereby, generating a new cash flow stream for forest owners. Upon harvesting of the post-1989 forests, the proportionate amount of carbon credits must be surrendered by the forest owner. The required credits could be purchased from domestic or international carbon markets at the market price (Ministry of Agriculture and Forestry, 2011a). This paper outlines a literature review of infinite rotation forestry methods, namely NPV/LEV and Real Options. This is followed by a review of carbon forestry literature, with a focus on carbon forestry modeling work in New Zealand. The methodology employed in this paper is described, along with data used and assumptions made. Valuation results are presented and discussed. We conclude with a scenario analysis of potential implications in New Zealand. A key original contribution of this paper to existing literature is the development of a double RV Binomial Tree (Real Options) method to analyze carbon forestry in New Zealand. This method enables simultaneous modeling of both the timber and carbon prices stochastically. A further contribution is the scenario analysis of potential implications on existing post-1989 radiata pine forests and the annual carbon stock change in New Zealand. 1 It is noted here that some owners of pre-1990 forest land are eligible for a free allocation of carbon credits. This type of allocation is a one-off compensation and is not considered in this paper since the focus here is on new post- 1989 forests. 2 Carbon stock accumulated between 1st January 1990 and 31st December 2007 does not earn any credits, nor does it incur any liabilities. 2 Infinite Rotation Forestry Valuation Methods Fixed Rotation Forestry Valuation Probably the best known and still quite widely adopted net present value (NPV) approach by Faustmann (1849), the value of the forest investment is determined by forecasting expected future cash flows and discounting them at a specific discount rate. This method attempts to account for riskiness in the investment and time value of money. It is relatively simple numerically, with a relatively easy implementation. However, it has a few notable weaknesses. Often, adjustments for risks are captured by the discount rate, which is assumed to be constant throughout the forest’s lifetime3. The NPV approach does not account for flexibility due to the assumption of a fixed investment path and duration, where the decision is made in advance, and remains unchanged, even when unexpected favourable or unfavourable events arise. It also ignores the value that alternative opportunities and choices bring to the investment such as deferring harvest or conversion to agriculture land. Flexible Rotation Forestry Valuation Flexibility in decision-making is valuable when investors face risks and uncertainty about the future, especially when there is a degree of irreversibility attached to the decisions being made (Dixit and Pindyck, 1995). Consider the situation in forestry where forest owners must decide when to harvest. Under the Faustmann NPV approach, the harvesting decision (based on the optimal rotation age calculated from the NPV) is made regardless of the timber price at the time of expected harvest (i.e. it is already pre-decided upfront when the trees were first planted). The decision to replant will also have to be made immediately after cutting, as per the optimal rotation plan. In addition, the harvesting decision is irreversible. Once harvested, trees of that age and size cannot be put back into the ground. If the timber price is low during the harvest, the "loss" in profits is also permanently irreversible. That is, an amount of money equivalent to the expected profit cannot be relied upon for any other investment. Given that forest owners face uncertainty in future prices and irreversibility in the consequences of their decisions, it may be advantageous for them to remain flexible about the timing of forest harvesting decisions. If timber prices are low at the anticipated time of harvest, forest owners may want to delay harvest, and wait-and-see before making a harvesting decision. Likewise, if timber prices are unusually high before the anticipated time of harvest, forest owners may want to harvest earlier than planned to take advantage of the high timber prices. Uncertainty and irreversibility of an investment decision cannot be easily introduced into and anticipated by the NPV approach. In practice, the optimal rotation age is recalculated as a stand matures, using 3 This is common, but is not always the case. It is noted here that the New Zealand Institute of Forestry’s Forest Valuation Standards (p A4-22) specifies that “the preferred approach in this situation is to adjust future cash flows rather than the discount rate”. updated information about timber prices as well as actual yields from the inventory (rather than the growth model) and costs. In order to better manage the true potential of the returns, forest owners should use a decision framework that can accommodate a flexible investment decision. The Real Options approach offers such flexibility. The Real Options Approach to Valuation Black and Scholes (1973) and Merton (1973) pioneered a formula for valuing a financial option and opened up subsequent research on the pricing of financial assets. This work paved the way for the development of Real Options theory by Myers (1977), who had the seminal idea that one can view a firm's discretionary investment opportunities as a call option on real assets, in much the same way as a financial call option provides decision rights on financial assets. As an analogy, a Real Option can have its underlying asset as the gross project value of expected operating cash flows, its exercise price as the investment required to obtain this underlying asset, and the time to maturity as the period of time during which the decision maker can defer the investment before the investment opportunity expires. In short, Real Options are investments in real assets (as opposed to financial assets), which confer the investor the right, but not the obligation, to undertake certain actions in the future (Schwartz and Trigeorgis, 2004). There are three general approaches for implementing Real Options valuations: . Partial Differential Equation (PDE): The PDE approach treats time as a continuous variable and expresses the present value of a cash flow stream as the solution to a PDE. The most famous such PDE appears in Black and Scholes (1973). This is the standard and most widely used Real Options valuation method in the academic literature research due to its mathematical elegance and insights. For example, Pindyck (1993) studied the uncertain cost of investment in nuclear power plants, from which he derived a decision rule for irreversible investments subject to technical and input uncertainties.
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